Abstract

We have performed off-axis heterodyne holography with very weak illumination by recording holograms of the object with and without object illumination in the same acquisition run. We have experimentally studied how the reconstructed image signal (with illumination) and noise background (without) scale with the holographic acquisition and reconstruction parameters that are the number of frames and the number of pixels of the reconstruction spatial filter. The first parameter is related to the frequency bandwidth of detection in time, the second one to the bandwidth in space. The signal to background ratio varies roughly like the inverse of the bandwidth in time and space. We have also compared the noise background with the theoretical shot-noise background calculated by Monte Carlo simulation. The experimental and Monte Carlo noise background agree very well with each other.

© 2013 Optical Society of America

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  15. Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. French, D. Nolte, and M. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett. 26, 334–336 (2001).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (2)

2010 (3)

2009 (1)

2008 (2)

2007 (3)

2006 (3)

2005 (4)

2004 (1)

2003 (1)

2002 (4)

2001 (3)

2000 (3)

1999 (1)

1998 (4)

T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

M. Newberry, “Measuring the gain of a CCD camera,” Axiom Tech. Note 1, 1–8 (1998).

T. Kreis, W. Jueptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45–54 (1998).
[CrossRef]

1997 (2)

T. Kreis and W. Jueptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef]

1994 (2)

1971 (1)

A. Macovski, “Considerations of television holography,” J. Mod. Opt. 18, 31–39 (1971).
[CrossRef]

1967 (1)

J. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

1965 (1)

E. Leith, J. Upatnieks, and K. Haines, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. A 55, 981–986 (1965).
[CrossRef]

1949 (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London A 197, 454–487 (1949).
[CrossRef]

Abboud, M.

Absil, E.

Absil, É.

Al-Koussa, M.

Ansari, Z.

Atlan, M.

Bachor, H. A.

H. A. Bachor, A Guide to Experiment in Quantum Optics(Wiley, 1998).

Beghuin, D.

Bevilacqua, F.

Boccara, A.

Bun, P.

Charrière, F.

Collot, L.

Colomb, T.

Coppey-Moisan, M.

Cuche, E.

Dahlgren, P.

Davenport, W.

W. Davenport and W. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, 1958).

Depeursinge, C.

Desbiolles, P.

Dolecek, R.

P. Psota, V. Lédl, R. Doleček, J. Václavík, and M. Šulc, “Comparison of digital holographic method for very small amplitudes measurement with single point laser interferometer and laser Doppler vibrometer,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), paper DSu5B.3.

Doval, A.-F.

A.-F. Doval, “A systematic approach to TV holography,” Meas. Sci. Technol. 11, R1–R36 (2000).
[CrossRef]

Dunn, A.

Emery, Y.

Forget, B.

Fournier, D.

French, P.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London A 197, 454–487 (1949).
[CrossRef]

Geldmacher, J.

T. Kreis, W. Jueptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45–54 (1998).
[CrossRef]

Goodman, J.

J. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Goy, P.

Gross, M.

F. Verpillat, F. Joud, P. Desbiolles, and M. Gross, “Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles,” Opt. Express 19, 26044–26055 (2011).
[CrossRef]

E. Absil, G. Tessier, M. Gross, M. Atlan, N. Warnasooriya, S. Suck, M. Coppey-Moisan, and D. Fournier, “Photothermal heterodyne holography of gold nanoparticles,” Opt. Express 18, 780–786 (2010).
[CrossRef]

N. Warnasooriya, F. Joud, P. Bun, G. Tessier, M. Coppey-Moisan, P. Desbiolles, M. Atlan, M. Abboud, and M. Gross, “Imaging gold nanoparticles in living cell environments using heterodyne digital holographic microscopy,” Opt. Express 18, 3264–3273 (2010).
[CrossRef]

F. Verpillat, F. Joud, M. Atlan, and M. Gross, “Digital holography at shot noise level,” J. Display Technol. 6, 455–464(2010).
[CrossRef]

F. Joud, F. Laloë, M. Atlan, J. Hare, and M. Gross, “Imaging a vibrating object by sideband digital holography,” Opt. Express 17, 2774–2779 (2009).
[CrossRef]

M. Atlan, M. Gross, P. Desbiolles, É. Absil, G. Tessier, and M. Coppey-Moisan, “Heterodyne holographic microscopy of gold particles,” Opt. Lett. 33, 500–502 (2008).
[CrossRef]

M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909–911 (2007).
[CrossRef]

M. Gross, P. Goy, B. Forget, M. Atlan, F. Ramaz, A. Boccara, and A. Dunn, “Heterodyne detection of multiply scattered monochromatic light with a multipixel detector,” Opt. Lett. 30, 1357–1359 (2005).
[CrossRef]

M. Gross, P. Goy, and M. Al-Koussa, “Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging,” Opt. Lett. 28, 2482–2484 (2003).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Synthetic-aperture experiment in visible with on-axis digital heterodyne holography,” Opt. Lett. 26, 1550–1552 (2001).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Numerical heterodyne holography using 2D photo-detector arrays,” Opt. Lett. 25, 716–718 (2000).
[CrossRef]

Gu, Y.

Haines, K.

E. Leith, J. Upatnieks, and K. Haines, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. A 55, 981–986 (1965).
[CrossRef]

Hare, J.

Hayasaki, Y.

Ida, T.

Javidi, B.

Jones, R.

Joud, F.

Jueptner, W.

T. Kreis, W. Jueptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45–54 (1998).
[CrossRef]

T. Kreis and W. Jueptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Jüptner, W.

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef]

Kato, J.

Kim, M.

Kreis, T.

T. Kreis, W. Jueptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45–54 (1998).
[CrossRef]

T. Kreis and W. Jueptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kühn, J.

Laloë, F.

Lawrence, R.

J. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

LeClerc, F.

Lédl, V.

P. Psota, V. Lédl, R. Doleček, J. Václavík, and M. Šulc, “Comparison of digital holographic method for very small amplitudes measurement with single point laser interferometer and laser Doppler vibrometer,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), paper DSu5B.3.

Leith, E.

E. Leith, J. Upatnieks, and K. Haines, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. A 55, 981–986 (1965).
[CrossRef]

Leval, J.

Macovski, A.

A. Macovski, “Considerations of television holography,” J. Mod. Opt. 18, 31–39 (1971).
[CrossRef]

Magistretti, P. J.

Marquet, P.

Massatsch, P.

Massig, J. H.

Matsumura, T.

Melloch, M.

Meng, H.

Mizuno, J.

Montfort, F.

Murata, S.

Newberry, M.

M. Newberry, “Measuring the gain of a CCD camera,” Axiom Tech. Note 1, 1–8 (1998).

Nishida, N.

Nitanai, E.

Nolte, D.

Nomura, T.

Numata, T.

Ohta, S.

Picart, P.

Psota, P.

P. Psota, V. Lédl, R. Doleček, J. Václavík, and M. Šulc, “Comparison of digital holographic method for very small amplitudes measurement with single point laser interferometer and laser Doppler vibrometer,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), paper DSu5B.3.

Pu, Y.

Ramaz, F.

Rappaz, B.

Root, W.

W. Davenport and W. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, 1958).

Schnars, U.

Suck, S.

Šulc, M.

P. Psota, V. Lédl, R. Doleček, J. Václavík, and M. Šulc, “Comparison of digital holographic method for very small amplitudes measurement with single point laser interferometer and laser Doppler vibrometer,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), paper DSu5B.3.

Tamano, S.

Tessier, G.

Tziraki, M.

Upatnieks, J.

E. Leith, J. Upatnieks, and K. Haines, “Microscopy by wavefront reconstruction,” J. Opt. Soc. Am. A 55, 981–986 (1965).
[CrossRef]

Václavík, J.

P. Psota, V. Lédl, R. Doleček, J. Václavík, and M. Šulc, “Comparison of digital holographic method for very small amplitudes measurement with single point laser interferometer and laser Doppler vibrometer,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), paper DSu5B.3.

Verpillat, F.

Verrier, N.

Warnasooriya, N.

Yamaguchi, I.

Yamashita, K.

Yokota, M.

Yu, L.

Zhang, T.

Appl. Opt. (9)

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
[CrossRef]

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27–37 (2002).
[CrossRef]

P. Massatsch, F. Charrière, E. Cuche, P. Marquet, and C. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. 44, 1806–1812 (2005).
[CrossRef]

S. Tamano, Y. Hayasaki, and N. Nishida, “Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium,” Appl. Opt. 45, 953–959 (2006).
[CrossRef]

I. Yamaguchi, T. Ida, M. Yokota, and K. Yamashita, “Surface shape measurement by phase-shifting digital holography with a wavelength shift,” Appl. Opt. 45, 7610–7616 (2006).
[CrossRef]

F. Charrière, T. Colomb, F. Montfort, E. Cuche, P. Marquet, and C. Depeursinge, “Shot-noise influence on the reconstructed phase image signal-to-noise ratio in digital holographic microscopy,” Appl. Opt. 45, 7667–7673 (2006).
[CrossRef]

N. Verrier and M. Atlan, “Off-axis digital hologram reconstruction: some practical considerations,” Appl. Opt. 50, H136–H146 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

J. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Axiom Tech. Note (1)

M. Newberry, “Measuring the gain of a CCD camera,” Axiom Tech. Note 1, 1–8 (1998).

J. Display Technol. (1)

J. Mod. Opt. (1)

A. Macovski, “Considerations of television holography,” J. Mod. Opt. 18, 31–39 (1971).
[CrossRef]

J. Opt. Soc. Am. A (4)

Meas. Sci. Technol. (2)

A.-F. Doval, “A systematic approach to TV holography,” Meas. Sci. Technol. 11, R1–R36 (2000).
[CrossRef]

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Eng. (1)

T. Kreis and W. Jueptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Opt. Express (5)

Opt. Lett. (16)

M. Atlan, M. Gross, P. Desbiolles, É. Absil, G. Tessier, and M. Coppey-Moisan, “Heterodyne holographic microscopy of gold particles,” Opt. Lett. 33, 500–502 (2008).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Numerical heterodyne holography using 2D photo-detector arrays,” Opt. Lett. 25, 716–718 (2000).
[CrossRef]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef]

T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
[CrossRef]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005).
[CrossRef]

M. Gross, P. Goy, B. Forget, M. Atlan, F. Ramaz, A. Boccara, and A. Dunn, “Heterodyne detection of multiply scattered monochromatic light with a multipixel detector,” Opt. Lett. 30, 1357–1359 (2005).
[CrossRef]

L. Yu and M. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30, 2092–2094 (2005).
[CrossRef]

T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32, 481–483 (2007).
[CrossRef]

M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909–911 (2007).
[CrossRef]

I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting color digital holography,” Opt. Lett. 27, 1108–1110 (2002).
[CrossRef]

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 2179–2181 (2002).
[CrossRef]

M. Gross, P. Goy, and M. Al-Koussa, “Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging,” Opt. Lett. 28, 2482–2484 (2003).
[CrossRef]

Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. French, D. Nolte, and M. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett. 26, 334–336 (2001).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Synthetic-aperture experiment in visible with on-axis digital heterodyne holography,” Opt. Lett. 26, 1550–1552 (2001).
[CrossRef]

Proc. R. Soc. London A (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. London A 197, 454–487 (1949).
[CrossRef]

Proc. SPIE (1)

T. Kreis, W. Jueptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45–54 (1998).
[CrossRef]

Other (3)

P. Psota, V. Lédl, R. Doleček, J. Václavík, and M. Šulc, “Comparison of digital holographic method for very small amplitudes measurement with single point laser interferometer and laser Doppler vibrometer,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), paper DSu5B.3.

W. Davenport and W. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, 1958).

H. A. Bachor, A Guide to Experiment in Quantum Optics(Wiley, 1998).

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Figures (12)

Fig. 1.
Fig. 1.

(a) Digital holography setup: L, diode laser; BS1 and BS2, beam splitters; AOM1 and AOM2, acousto-optic modulators; O, objective; BE, beam expander; M, mirror; A, light attenuator. USAF, transmission USAF target to image; CCD, CCD camera. (b) Illumination beam amplitude (solid line) and phase (dashed line) as a function of the frame index.

Fig. 2.
Fig. 2.

(a) Intensity signal |H(x,y,z=0)|2 detected by the CCD camera. (b), (c) k-space intensity signal |H~(kx,ky,z=0)|2 without (b) and k-space filtering (c) with two filter sizes 400×400. (d) Reconstructed images |H(x,y,z=D)|2 of the USAF target. Display is in arbitrary log scale.

Fig. 3.
Fig. 3.

Intensity image (i.e., |H(x,y,D)|2) of the USAF target reconstructed from H1,1 (a), H2 (b), H4 (c), and H8 (d). Reconstruction with spatial filter 282×282 pixels.

Fig. 4.
Fig. 4.

Same as Fig. 3 with higher illumination: intensity image (i.e., |H(x,y,D)|2) of the USAF target reconstructed from H1,1 (a), H2 (b), H4 (c), and H8 (d). Reconstruction with spatial filter 282×282 pixels. Vertical axis units are e2 per pixel.

Fig. 5.
Fig. 5.

Intensity (i.e., |H(x,y,D)|2) along the AA white line of Fig. 3. The black curves correspond H1,1 (a), H2 (b), H4 (c), and H8 (d). The light-gray curves in the background correspond to H2 (a), H2 (b), H4 (c), and H8 (d). Reconstruction is made with a spatial filter of 282×282 pixels. Vertical axis units are e2 per pixel.

Fig. 6.
Fig. 6.

Same as Fig. 5 with higher illumination: intensity (i.e., |H(x,y,D)|2) along the AA white line of Fig. 4. The black curves correspond to H1,1 (a), H2 (b), H4 (c), and H8 (d). The light-gray curves in the background correspond to H2 (a), H2 (b), H4 (c), and H8 (d). Reconstruction is made with a spatial filter of 282×282 pixels.

Fig. 7.
Fig. 7.

Average intensity |H|2¯: (a) as a function of the number Nb of frames recorded with illumination—Nb=1 for H1,1 or H1,1, Nb=2 for H2 or H2,, and Nb=32 for H32 or H32—and (b) as a function of the area of the spatial filter (in pixel units). Even-frame curves are black; odd-frame curves are light gray.

Fig. 8.
Fig. 8.

Reciprocal space intensity image H~(kx,ky,0) obtained by FFT from H2 (two odd frames without object illumination), and typical location of the spatial filter (400×400 pixels).

Fig. 9.
Fig. 9.

Reconstructed image from H1,1 for a 400×400 pixels (a) and 100×100 pixels spatial filter (b).

Fig. 10.
Fig. 10.

Principle of calculation of the Monte Carlo odd frames In(x,y) from I1(x,y) recorded without object illumination.

Fig. 11.
Fig. 11.

Reconstructed images calculated from four frames recorded without object illumination, i.e., from H4 (a), and from four Monte Carlo frames, i.e., from H4 (b). Histogram of the intensity |H|2 displayed in linear (black) and logarithmic scale (light gray): without object illumination (c), and with Monte Carlo (d). The reconstruction is made with a 282×282 pixel spatial filter.

Fig. 12.
Fig. 12.

Average intensity |H|2¯ as a function of the number Nb of frames: Nb=2 for H2 or H2, Nb=4 for H4 or H4,, and Nb=32 for H32 or H32. The frames are either recorded without object illumination Hn or simulated by Monte Carlo Hn. The images have been reconstructed with 2FFT. The size of the spatial filter is 400×400, 282×282, 200×200, 141×141, and 100×100.

Equations (11)

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ωI=ωL+ωAOM1,ωLO=ωL+ωAOM2,
ωLOωI=ωAOM2ωAOM1=ωCCD/8.
H~(kx,ky,0)=FFT[H(x,y,0)].
H~(kx,ky,z)=H~(kx,ky,0)ej(kx2+ky2)z/k0,
H(x,y,z)=FFT1[H~(kx,ky,z)].
H2=I0I4,H4=(I0I4)+j(I2I6),H4K=k=0k=K1(I8kI8k+4)+j(I8k+2I8k+6),
H1,1=I0I1.
In(x,y)=I(x,y)+on(x,y).
on(x,y)=0,|on(x,y)|2=I(x,y).
on(x,y)=0,|on(x,y)|2I1(x,y).
In(x,y)=I1(x,y)+on(x,y).

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